Regression models are studied in survey data and are widely used to construct model-based estimators. Oftentimes, the relationships vary across different subjects or domains. Identifying a correct model structure with consideration of sampling weights is essential in making inferences and estimating population parameters. In this work, we propose the weighted clustered coefficients regression models for grouping covariate effects for survey data. The new method uses a weighted loss function and pairwise penalties on all pairs of observations. An algorithm based on the alternating direction method of multipliers algorithm is developed to obtain the estimates. We also study the theoretical properties of the estimator under the survey sampling setup. In the simulation study, the empirical performance of the proposed estimator is compared to the method without sampling weights, which suggests that sampling weights is important in identifying clusters in regression models.

翻译：回归模型在调查数据中研究,并广泛用于构建基于模型的测算器。通常,不同主题或领域之间的关系各不相同。确定正确的模型结构,同时考虑抽样权重,对于作出推论和估计人口参数至关重要。在这项工作中,我们提议了用于调查数据组合共变效应的加权组合系数回归模型。新方法使用加权损失函数,对所有观测对等观测进行配对处罚。根据乘数算法交替方向法开发了一种算法,以获得估计数。我们还研究了调查抽样结构下的估测器的理论特性。在模拟研究中,拟议的估测仪的经验性表现与没有抽样权重的方法相比较,这表明取样权重对于确定回归模型中的集体十分重要。